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  • 1.
    Fällström, Anders
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Algebras of bounded holomorphic functions1994Doktoravhandling, med artikler (Annet vitenskapelig)
    Abstract [en]

    Some problems concerning the algebra of bounded holomorphic functions from bounded domains in Cn are solved. A bounded domain of holomorphy Q in C2 with nonschlicht i7°°- envelope of holomorphy is constructed and it is shown that there is a point in Q for which Gleason’s Problem for H°°(Q) cannot be solved.

    If A(f2) is the Banach algebra of functions holomorphic in the bounded domain Q in Cn and continuous on the boundary and if p is a point in Q, then the following problem is known as Gleason’s Problem for A(Q) :

    Is the maximal ideal in A(Q) consisting of functions vanishing at p generated by (Zl ~Pl) , ■■■ , (Zn - Pn) ?

    A sufficient condition for solving Gleason’s Problem for A(Q) for all points in Q is given. In particular, this condition is fulfilled by a convex domain Q with Lipi+£-boundary (0 < e < 1) and thus generalizes a theorem of S.L.Leibenzon. One of the ideas in the methods of proof is integration along specific polygonal lines.

    If Gleason’s Problem can be solved in a point it can be solved also in a neighbourhood of the point. It is shown, that the coefficients in this case depends holomorphically on the points.

    Defining a projection from the spectrum of a uniform algebra of holomorphic functions to Cn, one defines the fiber in the spectrum over a point as the elements in the spectrum that projects on that point. Defining a kind of maximum modulus property for domains in Cn, some problems concerning the fibers and the number of elements in the fibers in certain algebras of bounded holomorphic functions are solved. It is, for example,

    shown that the set of points, over which the fibers contain more than one element is closed. A consequence is also that a starshaped domain with the maximum modulus property has schlicht /y°°-envelope of holomorphy. These kind of problems are also connected with Gleason’s problem.

    A survey paper on general properties of algebras of bounded holomorphic functions of several variables is included. The paper, in particular, treats aspects connecting iy°°-envelopes of holomorphy and some areas in the theory of uniform algebras.

  • 2.
    Gadde, Erland
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Stable iterated function systems1992Doktoravhandling, monografi (Annet vitenskapelig)
    Abstract [en]

    The purpose of this thesis is to generalize the growing theory of iterated function systems (IFSs). Earlier, hyperbolic IFSs with finitely many functions have been studied extensively. Also, hyperbolic IFSs with infinitely many functions have been studied. In this thesis, more general IFSs are studied.

    The Hausdorff pseudometric is studied. This is a generalization of the Hausdorff metric. Wide and narrow limit sets are studied. These are two types of limits of sequences of sets in a complete pseudometric space.

    Stable Iterated Function Systems, a kind of generalization of hyperbolic IFSs, are defined. Some different, but closely related, types of stability for the IFSs are considered. It is proved that the IFSs with the most general type of stability have unique attractors. Also, invariant sets, addressing, and periodic points for stable IFSs are studied.

    Hutchinson’s metric (also called Vaserhstein’s metric) is generalized from being defined on a space of probability measures, into a class of norms, the £-norms, on a space of real measures (on certain metric spaces). Under rather general conditions, it is proved that these norms, when they are restricted to positive measures, give rise to complete metric spaces with the metric topology coinciding with the weak*-topology.

    Then, IFSs with probabilities (IFSPs) are studied, in particular, stable IFSPs. The £-norm-results are used to prove that, as in the case of hyperbolic IFSPs, IFSPs with the most general kind of stability have unique invariant measures. These measures are ”attractive”. Also, an invariant measure is constructed by first ”lifting” the IFSP to the code space. Finally, it is proved that the Random Iteration Algorithm in a sense will ”work” for some stable IFSPs.

  • 3.
    Lundgren, Christina
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap. Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Lust till matematik - en rättighet eller bara några få förunnat?2010Independent thesis Advanced level (professional degree), 20 poäng / 30 hpOppgave
    Abstract [sv]

    Denna studie är genomfört som ett undervisningsförsök, där formativ bedömning har imple­menterats i matematikundervisning. Syftet med studien var att studera om det var möjligt att förändra undervisningen på denna korta tid samt om eleverna blev mer motiverade och om de upplevde mer lust till ämnet genom denna undervisningsstrategi. Ett särskilt fokus riktades på elever i matematiksvårigheter.

     

    Studien genomfördes i en årskurs 7:a, under höstterminen 2009, med inspiration Wiliam, (2007) Five ”Key Strategies” for Effective Assessmentutifrån och Black et al. (2003), Assess­ment for Learning – Putting it into practice. De förändringar som gjordes genomfördes av den ordinarie matematikläraren med stöd av mig som handledare under hela försöksperioden.

     

    För metodinsamling valdes, enkät, observation och intervju för att därigenom kunna göra en triangulerad ansats. Både enkät och intervju gjordes som för- och eftermätning och riktades mot eleverna. Observationer gjordes även de före försöket i avseende på att studera lärarens undervisning och de utvalda elevernas beteende och effektiva arbetstid i klassrummet. Däref­ter gjordes fortlöpande observationer under hela försökets gång. Av klassens 15 elever valde 14 att ställa upp i undersökningen.

     

    Förändringar tar tid, vilket medför att resultatet inte blev häpnadsväckande men visade ändå på tendenser till att elevernas motivation och lust till matematiken ökade genom implemente­ring av formativ bedömning i undervisningen.

  • 4.
    Nordekvist, Kristoffer
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Preparation for a Laboratory Exercise: the effects of writing a summary2009Independent thesis Advanced level (professional degree), 10 poäng / 15 hpOppgave
    Abstract [en]

    This degree project has studied how a changed preparation affected students' outcome of a laboratory exercise. Through use of cognitive load theory and sociocultural theory a guided writing of summary was designed. Students in secondary school were let to prepare for a laboratory exercise through a traditional teacher led introduction or the guided writing of summary. Data was collected as observations, worksheets, tests and evaluations. Results suggest that the guided writing of summary facilitated a construction of cognitive schema supporting students' method. This made them follow instructions and understand purpose of the laboratory exercise before and during the exercise in a better way than students preparing through a teacher led introduction. Furthermore students' perception of aim of the exercise shifted from theoretical work afterwards to theoretical work before and practical work during the exercise. This shows an improved understanding of links between theory and practice.

  • 5.
    Persson, Helena
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Ekborg, Margareta
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för naturvetenskapernas och matematikens didaktik.
    Garpelin, Anders
    Mälardalens högskola, Sverige.
    Ämnesintegerrad undevisning i naturvetenskap - Vad är det?2009Inngår i: NorDiNa: Nordic Studies in Science Education, ISSN 1504-4556, Vol. 5, nr 1, 47-60 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Biology, chemistry and physics might be taught as separate subjects, but sometimes they are taught as combined with one another or with other subjects.  Nationally and internationally the concept integrated science teaching lacks a uniform definition. To find out more about how practicing teachers define and perform integrated teaching, interviews were undertaken with five teachers, teaching science in school year 7 to 9 (age 13-16) in the Swedish compulsory school. Two ways of integrating science teaching were found; one combining the science subjects and one combining the science subjects with other school subjects. Results showed differences in the ways of teaching integrated science, in the interpretation of what the teachers meant by science integrating teaching and which obstacles and possibilities they saw. Visions about working with integrated science in the future and how these visions correspond to teacher’s reality is also discussed.

  • 6.
    Popov, Oleg
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Developing outdoor physics project using the activity theory framework2008Inngår i: GIREP 2008 International Conference. University of Cyprus 18-22 August 2008: Physics curriculum design development and validation, 2008, ?- s.Konferansepaper (Fagfellevurdert)
    Abstract [en]

    This paper presents the conceptualisation, implementation and evaluation of methodology of “outdoor physics” a project in science teacher education at Umeå University, Sweden (see http://outdoorphysics.educ.umu.se). Activity Theory was used as the theoretical framework for project development. The fundamental constructs of this theory: collaborative activity, motivation, object and context of learning were taken into consideration in the development of outdoor cases and methodology of the project. Prospective science teachers took active part in all stages of project activities. They developed specific cases for outdoor study, tested these both by themselves and with students in schools and evaluated their outcomes. The various cases of outdoor physics were part of teacher students’ research projects presented at the end of their undergraduate studies. Professional development of prospective teachers of science participating in the project is the main outcome of the current stage of the project, which benefited from international collaboration with colleagues from Russia (KSPU, Petrozavodsk) and some European countries (OutLab project). We expect that the knowledge acquired by prospective teachers in outdoor physics activities can also lead to new pedagogical approaches in their future professional work.

  • 7.
    Österlund, Lise-Lotte
    et al.
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Ekborg, Margareta
    Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik, teknik och naturvetenskap.
    Students’ understanding of redox reactions in three situations2009Inngår i: NorDiNa: Nordic Studies in Science Education, ISSN 1504-4556, Vol. 5, nr 2, 115-127 s.Artikkel i tidsskrift (Fagfellevurdert)
    Abstract [en]

    Redox models that explain electrochemical issues have been found to be difficult to teach and to learn. The aim of this study was to investigate students’ reasoning about redox reactions in three situations, how they used the activity series of metals and if they transferred knowledge between domains. Semi-structured interviews were carried out with ten students on two different occasions and dealt with three situations 1) a laboratory practical on corrosion; 2) a demonstration of zinc and copper sulphate solution; and 3) a corroded sculpture. The results indicated that the electron model was fundamental and reinforced. The identification of the reducing agent in the situations was unproblematic. The students’ conceptions regarding the oxidizing agent varied and diverged from the scientific model in some situations. Depending on the situation, the activity series of metal became a tool as well as an obstacle. Some transfer of knowledge between the classroom and the outdoor situation was indicated.

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